settings>about tablet>status will show a serial number. however, this is NOT the serial number of your device for registration purposes. the sticker on the bottom of your Transformer next to the charging port should match the one on the box the unit came in. That is the serial number of your transformer.

My father-in-law had the unknown serial number problem. After a few back and forth emails from ASUS tech support they instructed him to return it to them at hi expense so they could fix it. He rightfully kicked up a stink about having to pay to send it to them and they agreed to pay for shipping. They received the device last week and it already shows as being on it's way back to him in Canada. So if you're still having this problem it seems that the only way to fix it is to send your Transformer in to them.